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Simplifying 9x2 + -41x + -40 = 0 Reorder the terms: -40 + -41x + 9x2 = 0 Solving -40 + -41x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -4.444444444 + -4.555555556x + x2 = 0 Move the constant term to the right: Add '4.444444444' to each side of the equation. -4.444444444 + -4.555555556x + 4.444444444 + x2 = 0 + 4.444444444 Reorder the terms: -4.444444444 + 4.444444444 + -4.555555556x + x2 = 0 + 4.444444444 Combine like terms: -4.444444444 + 4.444444444 = 0.000000000 0.000000000 + -4.555555556x + x2 = 0 + 4.444444444 -4.555555556x + x2 = 0 + 4.444444444 Combine like terms: 0 + 4.444444444 = 4.444444444 -4.555555556x + x2 = 4.444444444 The x term is -4.555555556x. Take half its coefficient (-2.277777778). Square it (5.188271606) and add it to both sides. Add '5.188271606' to each side of the equation. -4.555555556x + 5.188271606 + x2 = 4.444444444 + 5.188271606 Reorder the terms: 5.188271606 + -4.555555556x + x2 = 4.444444444 + 5.188271606 Combine like terms: 4.444444444 + 5.188271606 = 9.63271605 5.188271606 + -4.555555556x + x2 = 9.63271605 Factor a perfect square on the left side: (x + -2.277777778)(x + -2.277777778) = 9.63271605 Calculate the square root of the right side: 3.103661716 Break this problem into two subproblems by setting (x + -2.277777778) equal to 3.103661716 and -3.103661716.Subproblem 1
x + -2.277777778 = 3.103661716 Simplifying x + -2.277777778 = 3.103661716 Reorder the terms: -2.277777778 + x = 3.103661716 Solving -2.277777778 + x = 3.103661716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.277777778' to each side of the equation. -2.277777778 + 2.277777778 + x = 3.103661716 + 2.277777778 Combine like terms: -2.277777778 + 2.277777778 = 0.000000000 0.000000000 + x = 3.103661716 + 2.277777778 x = 3.103661716 + 2.277777778 Combine like terms: 3.103661716 + 2.277777778 = 5.381439494 x = 5.381439494 Simplifying x = 5.381439494Subproblem 2
x + -2.277777778 = -3.103661716 Simplifying x + -2.277777778 = -3.103661716 Reorder the terms: -2.277777778 + x = -3.103661716 Solving -2.277777778 + x = -3.103661716 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.277777778' to each side of the equation. -2.277777778 + 2.277777778 + x = -3.103661716 + 2.277777778 Combine like terms: -2.277777778 + 2.277777778 = 0.000000000 0.000000000 + x = -3.103661716 + 2.277777778 x = -3.103661716 + 2.277777778 Combine like terms: -3.103661716 + 2.277777778 = -0.825883938 x = -0.825883938 Simplifying x = -0.825883938Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.381439494, -0.825883938}
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